Laplace2DApp: 2D Laplace Temperature Solver GUI

AppDesigner Graphical User Interface to solve 2D Laplace temperature on a rectangle with Dirichlet/Neumann (constant or expression) BCs.

Laplace2DApp is a professional MATLAB AppDesigner-style GUI for solving the steady-state 2D Laplace equation for temperature on a rectangular domain:∂2T∂x2+∂2T∂y2=0\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0∂x2∂2T​+∂y2∂2T​=0

This corresponds to steady heat conduction in a homogeneous medium with no internal heat generation.

Key Features

• Rectangular domain: [0,Lx]×[0,Ly][0,Lx]\times[0,Ly][0,Lx]×[0,Ly]
• Finite-difference discretization on a uniform Cartesian grid (5-point Laplacian stencil for interior nodes)
• Boundary conditions per side (Left/Right/Bottom/Top):
• Dirichlet: T=g(x,y)T=g(x,y)T=g(x,y)
• Neumann: ∂T/∂n=q(x,y)\partial T/\partial n = q(x,y)∂T/∂n=q(x,y) using outward normal derivative
• Boundary values can be constants or spatially varying expressions using: x, y, Lx, Ly
• Direct solver (sparse backslash \) or Iterative solver (bicgstab)
• Visualization: Contour (with configurable levels) or Surface
• Export solution arrays to base workspace

How to Run

1. Download and unzip
2. In MATLAB, set folder as Current Folder (or add to path)
3. Run:

app = Laplace2DApp;

Boundary Condition Input (Concise Examples)

Expressions may use x, y, Lx, Ly. For arrays, use element-wise operators: .* ./ .^

Dirichlet examples

• Left: 100
• Right: 0
• Bottom: 50*sin(pi*x/Lx)
• Top: 100 + 20*cos(2*pi*x/Lx)

Neumann examples (outward ∂T/∂n\partial T/\partial n∂T/∂n)

• Insulated wall: 0
• Left varying: 10*cos(pi*y/Ly)
• Top varying: 5*sin(2*pi*x/Lx)

Neumann outward sign convention

• Left (x=0): outward is −x
• Right (x=Lx): outward is +x
• Bottom (y=0): outward is −y
• Top (y=Ly): outward is +y

GUI Parameters (What Each Option Does)

• Lx, Ly: domain lengths
• Nx, Ny: number of grid nodes (higher → more accurate, slower)
• Plot = Contour/Surface: 2D filled contours or 3D surface
• Levels: number of contour levels (Contour mode)
• Solver = Direct / Iterative: \ (robust) or bicgstab (efficient for large grids)
• Show grid: toggles plot grid display (visual aid only)
• Solve: builds system A T=bA\,T=bAT=b, solves, plots, and reports residual
• Reset: restores default demo values and clears plot
• Export: sends T_laplace, x_laplace, y_laplace to base workspace

Outputs (Export Button)

• T_laplace : temperature field (size Nx × Ny)
• x_laplace : x grid vector
• y_laplace : y grid vector

Author / Citation

Dr. Abdelhamid BOUHELAL — 06 January 2026

If you use this app in academic work, please cite it accordingly:

Abdelhamid Bouhelal (2026). Laplace2DApp: 2D Laplace Temperature Solver GUI (https://www.mathworks.com/matlabcentral/fileexchange/<...>), MATLAB Central File Exchange. Retrieved January 6, 2026.